A supercharger consume alot off power to make power while a turbo don't.

A turbo is supreme as long as you don't operate on low load.

Why not combine it in a two step configuration?

Supercharger as step one charging a 1bar and a turbo as second stage charging at 1bar.

The charger would feed the engine while the turbo is not in it's operational area. Once the turbo kick in it will take the load off the supercharger.

once the turbo is charging 0.5bar the supercharger will only have a delta p off 0.5 bar. once the turbo is charging with 1bar the delta p off the supercharger is 0bar and therfor only require power to compensate for loss in mekanism and not efficensy.

Think radical and not traditional.